The youngster has been handed plenty of gametime this season at right-back in the absence of Seamus Coleman, having started eight times in the Premier League.
Kenny found himself introduced to the first team during a difficult period under Ronald Koeman, while Everton also found it tough to turn results in a positive direction when David Unsworth was placed in temporary charge.
However, the Merseyside outfit now find themselves unbeaten in four in all competitions as they prepare to face Newcastle on Wednesday.
Everton have moved up to 10th in the table and Kenny believes Allardyce is a key reason for their turnaround on the field.
"We've had three wins and a draw so it's been brilliant for us and we want to keep that going into Wednesday [at Newcastle]," Kenny said.
"Once you start getting a couple of results you do kick on from there because when results aren't going for you you don't think anything will go for you.
"He [Allardyce] has just brought how he wants us to play against whoever it is and we have to adjust to different teams with different styles.
"He makes his instructions very clear on how he want us to play and his backroom staff are brilliant and we have great experience around us.
"For me coming through now, I think I am at the best place and I want to keep on playing and getting better and better."